Mathematics... is a bit like discovering oil. ... But mathematics has one great advantage over oil, in that no one has yet ... found a way that you can keep using the same oil forever.

Fermat said he had a proof.

But the best problem I ever found, I found in my local public library.

It's fine to work on any problem, so long as it generates interesting mathematics along the way - even if you don't solve it at the end of the day.

There are proofs that date back to the Greeks that are still valid today.

Just because we can't find a solution it doesn't mean that there isn't one.

I carried this problem around in my head basically the whole time. I would wake up with it first thing in the morning, I would be thinking about it all day, and I would be thinking about it when I went to sleep. Without distraction I would have the same thing going round and round in my mind.